The other half of western civilization:
An experiment in freshman science teaching
(The American Society for Cell Biology, 1 December 2007)
William Bialek
Joseph Henry Laboratories of Physics
Lewis-Sigler Institute for Integrative Genomics
Princeton Center for Theoretical Physics
Princeton University
http://www.princeton.edu/~wbialek/wbialek.html
How many cultures?
Literary intellectuals at one pole--at the other scientists,
and as the most representative, physical scientists.
Between the two a gulf of mutual incomprehension ... a
curious distorted image of each other.
CP Snow, in The Two Cultures and The Scientific Revolution
(Cambridge University Press, 1959)
Could there be as large a gulf within science itself?
The “mathematical sciences”
(e.g, physics)
The “non-mathematical sciences”
(e.g, biology)
There is a widespread (almost trite) sentiment that this
gulf between the physical and biological sciences needs to
bridged, and that now is the right time to do this.
“The biology of the 21st century will be a more quantitative science.”
“The greatest challenges need to be met by interdisciplinary collaborations.”
“The genome and the computer have revolutionized how we do biology.”
“As we address system-level questions, we move beyond what we can do
intuitively, and need more mathematical tools.”
“Mathematics will be biology’s new microscope.”
There is much less agreement about what all of this
actually means, even in principle.
“There’s something happening here, what it is ain’t exactly clear ...”
(Stephen Stills, Buffalo Springfield, 1967)
Before we have a theory, let’s look at the data ...
(middle pages of first articles in current issues)
The difference between physics and biology is not just that physics “makes more use
of quantitative methods” (although it does).
In physics, we are searching for an understanding of Nature that we can summarize in
mathematical terms.
Mathematics is not an optional accessory, nor is it merely a tool alongside many others.
“La filosofia è scritta in questo grandissimo libro che continuamente ci sta aperto innanzi a gli
occhi (io dico l'universo), ma non si può intendere se prima non s'impara a intender la lingua, e
conoscer i caratteri, né quali è scritto. Egli è scritto in lingua matematica, e i caratteri sono
triangoli, cerchi, ed altre figure geometriche, senza i quali mezi è impossibile a intenderne
umanamente parola; senza questi è un aggirarsi vanamente per un'oscuro laberinto.”
~”The book of Nature is written in the language of mathematics.”
(Galileo Galilei, 1623)
Two related but distinct goals
Educate biologists who find it natural to do quantitative experiments, sophisticated
analyses of their data, and meaningful comparisons with theory
(because biology is so big, even incremental progress can have a big impact)
(perhaps we shouldn’t be shy to say “make biology more like physics”)
Educate physicists who find it natural to bring the “physicist’s style of thought” to
study a broader class of systems, including biological systems
(this clearly can’t be accomplished by learning less physics!)
These goals are very different at the graduate level.
Given the state of biology education today, meaningful progress on the first goal is
hard to achieve if you wait until graduate school.
Similarly, if you wait too long to start work on the second goal one has to face large
barriers of language and habit
So: start at the beginning!
Boundary conditions
First, do no harm.
For the first year, we want to create an alternative to the combination of
freshman physics and chemistry ...
While we want lots of connections to biology, we don’t want the
responsibility of communicating the factual content of intro bio courses
(save this for a sophomore follow up course).
All relevant departments need to agree that we have delivered the
equivalent of freshman physics and chemistry (+ a little CS) at some level.
Thus, students from our course will have access to the full range of majors.
As in our physics courses for majors, we build on previous mathematical
experience, but will teach some of what we need as we go along.
We simplify our problem by taking students who have had a calculus course
at the level of AP Calculus BC.
You can’t satisfy the boundary conditions without
genuine collaboration among the departments.
In particular, a top down initiative won’t work.
(... There’s a man with a gun over there, telling me I got to beware ...)
We had the good fortune to have a group of faculty
from all the relevant departments who were interested
in rethinking freshman science education in the
broadest sense. We worked from a “zero base budget.”
Faculty
W Bialek (physics)
CG Callan (physics)
D Botstein (molecular biology)
B Chazelle (computer science)
JT Groves (chemistry)
M Hecht (chemistry)
L Hodges (teaching center)
L Kruglyak (evolutionary biology)
D Marlow (physics)
J Rabinowtiz (chemistry)
C Schutt (chemistry)
O Troyanskaya (computer science)
EF Wieschaus (molecular biology)
Lewis-Sigler fellows
M Dunham, E Pearlstein, WS Ryu & EM Schoetz (experimentalists)
M Desai & M Kaschube (theorists)
Plus ...
many teaching assistants from all departments
Freshman physics topics
Newtonian mechanics
Electricity and magnetism (up to Maxwell)
Waves
Thermodynamics and a little statistical physics
(sometimes) “Modern physics”
Freshman chemistry topics
Thermodynamics and chemical equilibrium
Reaction kinetics
A tour of the periodic table
Chemical potential, electrochemistry, ...
Orbitals, bonds, ...
There are obvious commonalities, and some more subtle
relationships through the common mathematical structures
Can we organize around these more general ideas?
What kinds of mathematical structures do we use in describing nature?
Functional relations
V = IR, Q = CV, F = -kx, F = -γv, ...
Dynamical models (differential equations)
Elements of classical mechanics (more viscosity than usual!), chemical
kinetics (including enzymes, approximations), ... stability and response in
genetic switches, resonance in the cell membrane, ...
Probabilistic models
Boltzmann distribution, connections to thermodynamics (more complex
examples, e.g. protein folding), but also genetics, ...
Fields
Electricity and magnetism, but also diffusion, ... pattern formation in
development, ...
The quantum world
(example) Six weeks on probabilistic models
Genes, combinations and probability (with some inference)
Gas laws and the Boltzmann distribution
Brownian motion and the reality of molecules
*Emergence and approximation
Chemical equilibria and thermodynamics
Entropy, from Carnot to Shannon
we aimed high: mathematical sophistication at the
level of our honors freshman physics course
Getting some help from the computer:
Exploring the combinatorics that leads to the Boltzmann distribution
Meanwhile, in the lab ...
¨
Delbruck-Luria
experiment with yeast
we meet weekly to keep labs,
lectures, problem sets, ...
all tied together
Direct measurements of Brownian motion
The pioneers (now seniors)
and this is after the final exam
This year: 49 students in the freshman class
~1/3 of Juniors majoring in Physics came through our course
~1/2 of students so far major in Molecular Biology, instantly the “go to”
people for quantitative analysis, changing what gets done in the labs